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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 06 Dec 2017 20:05:43 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/06/t15125871559zibg2401zl1rsb.htm/, Retrieved Mon, 13 May 2024 23:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308634, Retrieved Mon, 13 May 2024 23:44:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2017-12-06 19:05:43] [f1ade19563a25eb31edff11eb9af1158] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72,9
85
98,8
86,3
101,9
95,1
71,6
84,4
97,5
100,7
92,9
74,4
81,4
84
95,9
86,8
98,9
101,3
74,5
86
92,6
103,5
90
68
79,7
81,2
91,8
96,5
93,2
98,9
79,2
79,2
99,4
105
88,3
65,3
78,1
82,3
93,8
96
89,2
99,2
81,7
76
101,1
103,5
84,5
74
78,3
83
100,9
95,4
89
109,5
77,5
83,4
104,6
101,4
93
81,7
80
85,5
95,2
102,7
96,2
113,8
76,8
88,9
109,2
101,4
99,1
84,1
87,9
90
108,5
99,5
111,3
117,5
82,7
94,9
115,2
116,6
110,1
88,5
100,1
102,9
120,1
108,2
114,4
123,5
92,3
101,1
114,8
127
112,4
85,3
109,2
113,7
110,4
127,3
117,4
124,6
100,7
93,5
124,5
121,7
98
81,6
82,7
86,8
104
99,4
94,9
110
85,2
85,7
112,4
110,9
95,7
77,1
80,2
84,5
112,8
107,3
100,6
123
89,1
93,9
115,9
113,1
102,4
77,2
91,7
99,7
120,9
104,7
120,3
112,1
83,7
98,1
119,1
108,5
108,5
86
91,2
92
113,9
100,7
107,3
115
87,6
95,9
106,9
113,9
101,9
75,8
83,6
88,7
97,9
105,6
105,2
111,1
92,5
88,3
107
112,7
95,5
78,7
93,2
91,5
102,8
107
98,5
108,8
90,9
85,6
111,9
111,9
93,3
77,8
88,4
92,7
109,6
103,4
96,5
117,5
90,7
86,7
107,5
109,5
94,7
78,7
89,1
97,3
106,6
106,9
102,7
116,3
84,5
92,9
110,7
104,1
99,1
86,9
88,4
97,9
116,9
100,8
112,8
118,8
84,4
95,5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308634&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308634&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
188.458333333333311.037412273579830.3
288.57510.731442756515235.5
388.141666666666711.428231258465639.7
488.283333333333310.259614854842129.5
591.47510.912138778776332
694.408333333333311.567702556006637
7101.89166666666712.706723941808734.8
8108.50833333333312.609409065047341.7
9110.21666666666714.262400240003845.7
1095.412.064146731685435.3
1110015.029728117059445.8
12104.44166666666712.877920380765437.2
13100.17512.11198692505639.2
1497.233333333333311.152605348554534
1597.766666666666710.89740030160134.1
1697.991666666666711.494382686048638.8
1799.75833333333339.9266819809801131.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 88.4583333333333 & 11.0374122735798 & 30.3 \tabularnewline
2 & 88.575 & 10.7314427565152 & 35.5 \tabularnewline
3 & 88.1416666666667 & 11.4282312584656 & 39.7 \tabularnewline
4 & 88.2833333333333 & 10.2596148548421 & 29.5 \tabularnewline
5 & 91.475 & 10.9121387787763 & 32 \tabularnewline
6 & 94.4083333333333 & 11.5677025560066 & 37 \tabularnewline
7 & 101.891666666667 & 12.7067239418087 & 34.8 \tabularnewline
8 & 108.508333333333 & 12.6094090650473 & 41.7 \tabularnewline
9 & 110.216666666667 & 14.2624002400038 & 45.7 \tabularnewline
10 & 95.4 & 12.0641467316854 & 35.3 \tabularnewline
11 & 100 & 15.0297281170594 & 45.8 \tabularnewline
12 & 104.441666666667 & 12.8779203807654 & 37.2 \tabularnewline
13 & 100.175 & 12.111986925056 & 39.2 \tabularnewline
14 & 97.2333333333333 & 11.1526053485545 & 34 \tabularnewline
15 & 97.7666666666667 & 10.897400301601 & 34.1 \tabularnewline
16 & 97.9916666666667 & 11.4943826860486 & 38.8 \tabularnewline
17 & 99.7583333333333 & 9.92668198098011 & 31.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308634&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]88.4583333333333[/C][C]11.0374122735798[/C][C]30.3[/C][/ROW]
[ROW][C]2[/C][C]88.575[/C][C]10.7314427565152[/C][C]35.5[/C][/ROW]
[ROW][C]3[/C][C]88.1416666666667[/C][C]11.4282312584656[/C][C]39.7[/C][/ROW]
[ROW][C]4[/C][C]88.2833333333333[/C][C]10.2596148548421[/C][C]29.5[/C][/ROW]
[ROW][C]5[/C][C]91.475[/C][C]10.9121387787763[/C][C]32[/C][/ROW]
[ROW][C]6[/C][C]94.4083333333333[/C][C]11.5677025560066[/C][C]37[/C][/ROW]
[ROW][C]7[/C][C]101.891666666667[/C][C]12.7067239418087[/C][C]34.8[/C][/ROW]
[ROW][C]8[/C][C]108.508333333333[/C][C]12.6094090650473[/C][C]41.7[/C][/ROW]
[ROW][C]9[/C][C]110.216666666667[/C][C]14.2624002400038[/C][C]45.7[/C][/ROW]
[ROW][C]10[/C][C]95.4[/C][C]12.0641467316854[/C][C]35.3[/C][/ROW]
[ROW][C]11[/C][C]100[/C][C]15.0297281170594[/C][C]45.8[/C][/ROW]
[ROW][C]12[/C][C]104.441666666667[/C][C]12.8779203807654[/C][C]37.2[/C][/ROW]
[ROW][C]13[/C][C]100.175[/C][C]12.111986925056[/C][C]39.2[/C][/ROW]
[ROW][C]14[/C][C]97.2333333333333[/C][C]11.1526053485545[/C][C]34[/C][/ROW]
[ROW][C]15[/C][C]97.7666666666667[/C][C]10.897400301601[/C][C]34.1[/C][/ROW]
[ROW][C]16[/C][C]97.9916666666667[/C][C]11.4943826860486[/C][C]38.8[/C][/ROW]
[ROW][C]17[/C][C]99.7583333333333[/C][C]9.92668198098011[/C][C]31.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308634&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
188.458333333333311.037412273579830.3
288.57510.731442756515235.5
388.141666666666711.428231258465639.7
488.283333333333310.259614854842129.5
591.47510.912138778776332
694.408333333333311.567702556006637
7101.89166666666712.706723941808734.8
8108.50833333333312.609409065047341.7
9110.21666666666714.262400240003845.7
1095.412.064146731685435.3
1110015.029728117059445.8
12104.44166666666712.877920380765437.2
13100.17512.11198692505639.2
1497.233333333333311.152605348554534
1597.766666666666710.89740030160134.1
1697.991666666666711.494382686048638.8
1799.75833333333339.9266819809801131.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.568582530009709
beta0.127508104014256
S.D.0.038787111983107
T-STAT3.28738329550779
p-value0.00498623486075585

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.568582530009709 \tabularnewline
beta & 0.127508104014256 \tabularnewline
S.D. & 0.038787111983107 \tabularnewline
T-STAT & 3.28738329550779 \tabularnewline
p-value & 0.00498623486075585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308634&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.568582530009709[/C][/ROW]
[ROW][C]beta[/C][C]0.127508104014256[/C][/ROW]
[ROW][C]S.D.[/C][C]0.038787111983107[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.28738329550779[/C][/ROW]
[ROW][C]p-value[/C][C]0.00498623486075585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308634&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.568582530009709
beta0.127508104014256
S.D.0.038787111983107
T-STAT3.28738329550779
p-value0.00498623486075585






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.16369138063443
beta1.01172954370464
S.D.0.308677639977375
T-STAT3.27762498047735
p-value0.00508698649580968
Lambda-0.0117295437046376

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.16369138063443 \tabularnewline
beta & 1.01172954370464 \tabularnewline
S.D. & 0.308677639977375 \tabularnewline
T-STAT & 3.27762498047735 \tabularnewline
p-value & 0.00508698649580968 \tabularnewline
Lambda & -0.0117295437046376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308634&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.16369138063443[/C][/ROW]
[ROW][C]beta[/C][C]1.01172954370464[/C][/ROW]
[ROW][C]S.D.[/C][C]0.308677639977375[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.27762498047735[/C][/ROW]
[ROW][C]p-value[/C][C]0.00508698649580968[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0117295437046376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308634&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308634&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.16369138063443
beta1.01172954370464
S.D.0.308677639977375
T-STAT3.27762498047735
p-value0.00508698649580968
Lambda-0.0117295437046376


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')